Dynamics and intrinsic statistical fluctuations of a gene switch

We studied a simple gene regulatory network, the toggle switch. Specifically, we examined the means and statistical fluctuations in numbers of proteins. We found that when omega, the ratio of rates of protein-gene unbinding to protein degradation, was between approximately 10(-3) and approximately 10, the fluctuations were much larger than those we would have expected from Poisson statistics. In addition, we examined characteristic time values for system relaxation and found both that they increased with omega and that they have significant phase transition effects, with a secondary time scale appearing near the boundary between bistable and other phases. Last, we discuss the bistability of the toggle switch.     

Energy landscapes for adsorption of a protein-like HP chain as a function of native-state stability

Dynamic Monte Carlo (DMC) simulations of the adsorption of simple protein-like chains are used to more clearly define the molecular basis for the dependence of adsorption thermodynamics on the stability of the unique lowest-energy "native state" conformation of the chain. Arai and Norde were among the first to show that proteins of low native-state stability strongly denature upon adsorption to weakly attractive sorbent surfaces, while relatively modest changes in conformation are observed in stable proteins under identical adsorption conditions. When the protein has a low native-state stability, favorable adsorption entropies are typically observed in such systems, leading to the general belief that the chain gains conformational entropy during adsorption through a net reduction in intramolecular interactions specific to the native-state structure. Analysis of energy landscapes generated from our DMC simulation results show that a net loss in specific intramolecular interactions can lead to a positive delta(ads)S under certain adsorption conditions. However, the influence of chain conformation on delta(ads)S is found to correlate more directly with the manner in which the unique states of the system are distributed among the energy levels available to the adsorbed chain. Delta(ads)S is found to tend toward a maximum for adsorption processes described by thermally averaged energy landscapes in which the energy levels carrying the highest Boltzmann weights have a high degree of conformational degeneracy. This condition is met when the average interaction energy between the chain and the sorbent equals that between two hydrophobic segments of the chain.     

Valence fluctuations,crystal structure stability and the effects of alloying

The systematics of the effects of alloying on the valence of cerium are discussed. In addition to factors such as the size and valence of the substitute atom and resulting “lattice pressure” and motion of the f level, the possible role of crystal structure stability is examined. In particular, a detailed analysis of both on cerium site and off cerium site alloying of CePd₃ suggests that crystal structure stability considerations are of over-riding importance for this system. For the Cu₃Au structure, the existence of a maximum number N_max of electrons per formula unit, which is determined from studies of Zr(Rh,Pd)₃, allows one correctly to predict the concentrations at which trivalence and saturated valence occur in six related pseudobinary alloy systems. However, these predictions are based on a model which requires:

• 1.(a) that in the mixed valence regime the valence of cerium adjusts so that the total number of electrons per cell is constant at N_max, and
• 2.(b) that cerium be tetravalent in CeRh₃.

The latter requirement is in strong disagreement with studies using microscopic probes such as L_III, absorption, X-ray photoelectron spectroscopy (XPS) and bremsstrahlung isochromat spectroscopy (BIS). Nonetheless, the predictive ability of the model is striking and cannot be dismissed as merely fortuitous.     

The intrinsic stability of the noble gas-coordinated transition-metal complex ions.

Density-functional-theory and high-level ab initio calculations have been performed on the [AuXe4]2+ ion and some other hypothetical xenon-, krypton-, and argon-coordinated transition-metal complex cations in the gas phase. Geometry optimization at the QCISD(T) level using a (6s7p4d2f1g) basis set for Au and a (4s4p2d1f) set for Xe predicted Au-Xe bond lengths in good agreement with the AuXe4(2+)(Sb2F11-)2 crystal structure. The ligand-binding energies of the [AuXe4]2+, [AuXe4]3+, and [PtXe4]2+ ions were predicted to be 229, 565, and 233 kcal/mol, respectively, at the CCSD(T) level. It is found that higher-level correlation effects are important to obtain accurate geometry parameters. The calculated results also indicated that various trivalent, tetravalent, and hexavalent transition-metal complexes of xenon or krypton might also be intrinsically stable.     

Fused five-membered rings determine the stability of C60F60

The structure and stability of a set of (CF)60 isomers have been computed at the B3LYP/6-31G(d) density functional theory level. The most stable isomer (6, F4@C60F56) has tube-like structure with four endo C-F bonds and fused five-membered rings at the end of the tube, while the reported most stable cage structure (2, F8@C60F52) with eight endo C-F bonds is higher in energy by 22.6 kcal/mol. This is in contrast to the isolated pentagon rule for the stability of fullerenes. The mean bond dissociation energy of 6 is larger than those of the experimental known C60F36, C60F48, and graphite fluoride. The relative energy per CF unit of 6 to graphite fluoride (CF)n is 3.7 kcal/mol, which is smaller than that of C60 fullerene per carbon to graphite (about 9-10 kcal/mol).     

Unsteady state flux response: a method to determine the nature of the solute and gel layer in membrane filtration

The unsteady-state permeate flux response to a step change in transmembrane pressure is shown to result in unique flux–pressure profiles for the three types of solutes common in membrane ultrafiltration (UF): (a) solutes which exert an osmotic pressure but do not form a ‘gel’; (b) solutes which do not exert an osmotic pressure but form a ‘gel’ and (c) solutes which exert an osmotic pressure and also form a ‘gel’. It is also shown that for stirred cell UF, changes in the bulk feed solution properties (concentration, volume) are negligible on the time scale needed to attain a stable permeate flux. Unsteady-state permeate flux measurements could therefore be made at short filtration times so that the results would not be masked by changes in bulk properties.     

How ion properties determine the stability of a lipase enzyme in ionic liquids: a molecular dynamics study

The influence of eight different ionic liquid (IL) solvents on the stability of the lipase Candida antarctica lipase B (CAL-B) is investigated with molecular dynamics (MD) simulations. Considered ILs contain cations that are based either on imidazolium or guanidinium as well as nitrate, tetrafluoroborate or hexafluorophosphate anions. Partial unfolding of CAL-B is observed during high-temperature MD simulations and related changes of CAL-B regarding its radius of gyration, surface area, secondary structure, amount of solvent close to the backbone and interaction strength with the ILs are evaluated. CAL-B stability is influenced primarily by anions in the order NO(3)(-)? BF(4)(-) < PF(6)(-) of increasing stability, which agrees with experiments. Cations influence protein stability less than anions but still substantially. Long decyl side chains, polar methoxy groups and guanidinium-based cations destabilize CAL-B more than short methyl groups, other non-polar groups and imidazolium-based cations, respectively. Two distinct causes for CAL-B destabilization are identified: a destabilization of the protein surface is facilitated mostly by strong Coulomb interactions of CAL-B with anions that exhibit a localized charge and strong polarization as well as with polar cation groups. Surface instability is characterized by an unraveling of α-helices and an increase of surface area, radius of gyration and protein-IL total interaction strength of CAL-B, all of which describe a destabilization of the folded protein state. On the other hand, a destabilization of the protein core is facilitated when direct core-IL interactions are feasible. This is the case when long alkyl chains are involved or when particularly hydrophobic ILs induce major conformational changes that enable ILs direct access to the protein core. This core instability is characterized by a disintegration of β-sheets, diffusion of ions into CAL-B and increasing protein-IL van der Waals interactions. This process describes a stabilization of the unfolded protein state. Both of these processes reduce the folding free energy and thus destabilize CAL-B. The results of this work clarify the impact of ions on CAL-B stabilization. An extrapolation of the observed trends enables proposing novel ILs in which protein stability could be enhanced further.     

The influence of exocyclic phosphorous substituents on the intrinsic stability of four-membered heterophosphetes: a theoretical study

Four-membered heterophosphetes such as oxaphosphetes, thiaphosphetes, and azaphosphetes have long been considered desirable target molecules for organic chemists because of their interesting structural features. In spite of extensive investigation, only one azaphosphete and one thiaphosphete have been synthesized to date. In this paper, two possible conformers of these four-membered rings, as well as their open-ring phosphorane forms with a set of exocyclic substituents and a few ring heteroatoms were studied by molecular computations. The results suggested that the relative stability of these compounds is strongly dependent on the electronic effect of the exocyclic P-substituents. Three different types of exocyclic substituents X were recognized. However, only the strong electron-withdrawing substituents (X=F, CN, OCN, SCN) were able to stabilize the ring forms, providing the possibility to design stable heterophosphetes on the basis of the present computational results.     

Mass spectrometric studies on the intrinsic stability of destruxin E from Metarhizium anisopliae

Destruxins are of current interest as bioactive agents. They are cyclic hexadepsipeptides produced by fungi, the most common destruxins, A, B and E, differing in the structure of a side chain. Before they can be widely used, the potential risk of destruxins and their metabolites entering the human food chain must to be assessed; thus, knowledge of the structures of their degradation products is essential. Here we report a study aimed at identifying, by tandem mass spectrometry and accurate mass analysis, the products resulting from thermally and temporally induced degradation of destruxin E. The degradation products fell into two groups: those with relatively simple modifications of the side chain and those involving much more complex rearrangements. The structures of most of the degradation products were deduced from the MS data, with the major product being destruxin E diol: significantly, this compound had previously been reported to have only been produced as a metabolic product of enzyme action rather than as a simple degradation product as demonstrated here.     

An intrinsic radical stability scale from the perspective of bond dissociation enthalpies: a companion to radical electrophilicities

Bond dissociation enthalpies (BDEs) of a large series of molecules of the type A-B, where a series of radicals A ranging from strongly electrophilic to strongly nucleophilic are coupled with a series of 8 radicals (CH2OH, CH3, NF2, H, OCH3, OH, SH, and F) also ranging from electrophilic to nucleophilic, are computed and analyzed using chemical concepts emerging from density functional theory, more specifically the electrophilicities of the individual radical fragments A and B. It is shown that, when introducing the concept of relative radical electrophilicity, an (approximately) intrinsic radical stability scale can be developed, which is in good agreement with previously proposed stability scales. For 47 radicals, the intrinsic stability was estimated from computed BDEs of their combinations with the strongly nucleophilic hydroxymethyl radical, the neutral hydrogen atom, and the strongly electrophilic fluorine atom. Finally, the introduction of an extra term containing enhanced Pauling electronegativities in the model improves the agreement between the computed BDEs and the ones estimated from the model, resulting in a mean absolute deviation of 16.4 kJ mol(-1). This final model was also tested against 82 experimental values. In this case, a mean absolute deviation of 15.3 kJ mol(-1) was found. The obtained sequences for the radical stabilities are rationalized using computed spin densities for the radical systems.     

Non-nuclear attractor of electron density as a manifestation of the solvated electron

Two or more polar molecules can trap an excess electron either in a dipole-bound fashion where it is located outside of the cluster (dipole-bound electron) or inside the cluster (solvated electron). The topology of the electron density in dipole-bound and solvated-electron clusters has been examined for the paradigm (HF)3- cluster. As spatial confinement of the excess electron increases, a non-nuclear maximum (or attractor) of the electron density eventually forms, which suggests that the solvated electron can be described as a topological atom with its own set of physicochemical properties.     

The intrinsic line width of the plasmon resonances in metal microclusters at very low temperatures: quantal surface fluctuations

The line shape of the plasmon resonance in a cold, small sodium cluster (Na₈) is calculated taking into account its coupling to the quantal quadrupole fluctuations of the cluster shape. This coupling is found to give rise to a small damping factor (Γ/?ω₁～0.03, where ?ω₁ denotes the energy centroid and Γ the full width at half maximum of the resonance), and to an asymmetric line shape with Gaussian behaviour in the wings.     

Structure and dynamics of concentration fluctuations in a polymer blend solution under shear flow

The technique of small-angle light scattering (SALS) has been employed to investigate the time-dependent behavior of a single-phase, semidilute solution of polystyrene and polybutadiene in dioctyl phthalate under shear flow. Concentration fluctuations in the polymer blend solution are found to grow with time in the direction of flow, and their orientation angles evolve from 45° from the flow direction toward 0°, with the steady-state value being dependent on shear rate. SALS patterns are simulated using a modified Cahn-Hilliard-Cook model, with an additional collective restoring force to account for polymer elasticity. Predictions from this modified model for the orientation angles of the concentration fluctuations are in excellent agreement with the experimental results. Our model also predicts that the quiescent structure factor has a Gaussian form and that the steady-state orientation of the scattering patterns is dependent on shear rate. These predictions are also in good agreement with our experimental observations. © 1994 John Wiley & Sons, Inc.     

Observation of dynamically induced fluctuations of the photon flux and resolution of the broad luminescence band of Cs2TeBr6

A frequency-selective photon correlation experiment is carried out using the 10 K emission of microcrystalline Cs₂TeBr₆ as an example. The recording of dynamically inducedD-fluctuations allows to resolve the vibrational fine structure of an electronic transition which is not obtained by usual emission spectroscopy at this temperature. The experimental findings support the physical relevance of Prigogine's star-unitary transformations.Dedicated to Professor Dr. Hermann Hartmann on the occasion of his seventieth birthday     

Diffusion in a Potential Field under the Gaussian-Sink Action: Analytical Solution of the Problem

A method for analytical solution of a base model, which reduces to a diffusion equation with a Gaussian-sink term in the electron transfer theory, is described. The method is constructed as a generalization of the Kramers approach to the problems on the high barrier crossing and is applicable to situations where the reaching of the reaction zone is of activation nature. The derived formulas span a very broad range of variations in the solvent adjustment rate, provided certain conditions as to the sink's width and center position are satisfied. In this range the kinetics is single-exponential and the rate constant is perceptibly smaller than the equilibrium estimate and steadily decreases if the adjustment slows down.     

Complex and chaotic oscillations in a model for the catalytic hydrogen peroxide decomposition under open reactor conditions

Numerous periodic and aperiodic dynamic states obtained in a model for hydrogen peroxide decomposition in the presence of iodate and hydrogen ions (the Bray-Liebhafsky reaction) realized in an open reactor (CSTR), where the flow rate was the control parameter, have been investigated numerically. Between two Hopf bifurcation points, different simple and complex oscillations and different routes to chaos were observed. In the region of the mixed-mode evolution of the system, the transitions between two successive mixed-mode simple states are realized by period-doubling of the initial state leading to a chaotic window in which the next dynamic state emerges mixed with the initial one. It appears in increasing proportions in concatenated patterns until total domination. Thus, with increasing flow rate the period-doubling route to chaos was obtained, whereas with decreasing flow rate the peak-adding route to chaos was obtained. Moreover, in very narrow regions of flow rates, chaotic mixtures of mixed-mode patterns were observed. This evolution of patterns repeats until the end of the mixed-mode region at high flow rates that corresponds to chaotic mixtures of one large and many small amplitude oscillations. Starting from the reverse Hopf bifurcation point and decreasing the flow rate, simple small amplitude sinusoidal oscillations were encountered and then the period-doubling route to chaos. With a further decreasing flow rate, the mixed-mode oscillations emerge inside the chaotic window.     

Quantum-chemical investigation of the factors which determine stability of the 3,5-dimethyl-1H-pyrazole-4-diazonium ion

It was shown by MNDO calculations that the stability of the 3,5-dimethyl-1H-pyrazole-4-diazonium ion to decomposition with the elimination of nitrogen is due to the destabilization of the formed carbocation, which has a triplet ground electronic state.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 349–351, March, 1990.     

Assessing the contribution of natural sources to the global mercury cycle: the importance of intercomparing dynamic flux measurements

In order to constrain the contribution of natural sources of mercury to the global atmospheric cycle we need to: 1. assess the methods used to measure mercury flux, 2. characterize those factors most important in controlling emissions, 3. develop a database of emissions from representative locations, and 4. develop a means of scaling up measured emissions to estimate fluxes on a regional basis. This paper describes how an international multi-collaborator project, the Nevada SToRMS Project, held September 1997 in Reno, Nevada, USA, contributed to our ability to constrain natural source mercury emissions. This study entailed a field intercomparison of those methods typically applied to measure mercury flux from substrate combined with evening workshops and round-table discussions. The project was unique in that it focused on assessing our ability to measure the flux of an environmental contaminant. This is more difficult than measurement of the concentration of a contaminant because of the number and nature of the variables which influence the field flux measurements, including experimental design, spatial heterogeneity, and temporally changing environmental conditions. As a result of the Nevada SToRMS Project, rapid and significant advances in our understanding of how to constrain emission fluxes from large areas of mercury enrichment were realized. Because this intercomparison was a multi-investigator project, the results and implications of the project have been broadly circulated. The sincere scientific collaboration that evolved amongst those working on the study has led to significant advancements in our understanding of the fate and transport of mercury in the environment.     

Potential of mean force between a large solute and a biomolecular complex: a model analysis on protein flux through chaperonin system

Insertion of a large solute into an even larger vessel comprising biopolymers followed by release of the same solute from it is one of the important functions sustaining life. As a typical example, an unfolded protein is inserted into a chaperonin from bulk aqueous solution, a cochaperonin acting as a lid is attached to the chaperonin rim and the protein folds into its native structure within the closed cavity, the cochaperonin is detached after the folding is finished, and the folded protein is released back to the bulk solution. On the basis of the experimental observations manifesting that the basic aspects of the protein flux through the chaperonin system is independent of the chaperonin, cochaperonin, and protein species, we adopt a simple model system with which we can cover the whole cycle of the protein flux. We calculate the spatial distribution of the solvent-mediated potential of mean force (PMF) between a spherical solute and a cylindrical vessel or vessel/lid complex. The calculation is performed using the three-dimensional integral equation theory, and the PMF is decomposed into energetic and entropic components. We argue that an unfolded protein with a larger excluded volume (EV) and weak hydrophobicity is entropically inserted into the chaperonin cavity and constrained within a small space almost in its center. The switch from insertion to release is achieved by decreasing the EV and turning the protein surface hydrophilic in the folding process. For this release, in which the energetic component is a requisite, the feature that the chaperonin inner surface in the absence of the cochaperonin is not hydrophilic plays essential roles. On the other hand, the inner surface of the chaperonin/cochaperonin complex is hydrophilic, and the protein is energetically repelled from it: The protein remains constrained within the small space mentioned above without contacting the inner surface for correct folding. The structural and inner-surface properties of the chaperonin or complex are controlled by the adenosine triphosphate (ATP) binding to the chaperonin, hydrolysis of ATP into adenosine diphosphate (ADP) and Pi, and dissociation of ADP and Pi. The function of the chaperonin system is exhibited by synchronizing the chemical cycle of ATP hydrolysis with hydration properties of a protein in the water confined on the scale of a nanometer which are substantially different from those in the bulk water.